In prior known rolling bearings of this general type, one of the rings is comprised of several ring segments which carry the raceways. After the rolling elements have been inserted in place, the ring elements are secured together by means of threaded bolts or the like about the periphery of the segments. These ring segments have to be produced and fitted separately which means that manufacture of bearings of this type is relatively complicated and expensive. Furthermore, as a practice matter, it is often impossible to obtain the precise running behavior necessary for use in the rolling bearing in machine tools because of the unavoidable production tolerance differentials in the assembled ring elements. Additionally, the rigidity and stiffness of the known roller bearing leaves something to be desired in applications where the bearing is subjected to off-center or eccentric loads.